Continuum damage mechanics applied to numerical analysis of ship collisions

The elasto-plastic damage behaviors of functionally graded materials (FGM) subjected to thermal loading are analyzed by the finite element method using continuum damage mechanics. Lemaitre's damage model is employed to analyze the damage behavior of a FGM disk subjected to thermal shock and a FGM coating subjected to thermal cycle. The effect of FGM on the thermal damage is discussed through some numerical examples for industrial materials. Numerical results reveal the validity of the present method for the development and the evaluation of new FGMs.

Fiber reinforced polymer laminates are susceptible to transverse low velocity impact which can cause significant damages, such as matrix cracks, delamination and fiber breakage. A 3-Dimensional (3-D) finite element model (FEM) is presented for the progressive damage analysis of fiber reinforced laminates subjected to low velocity impact. The constitutive equations of material used in the FEM are based on the continuum damage mechanics (CDM). The modified HASHIN failure criterions are used in the material model to detect the initiation of all the failure modes of laminates. A simplified material stiffness degradation scheme is used to characterize the material degradation due to damages. The failure criterions and material degradation scheme have been incorporated in the software ABAQUS/Explicit through the user defined material subroutine VUMAT. The available experiments of thin carbon fiber reinforced epoxy laminates subjected to low velocity impact were used to validate the developed FEM. The good agreement of the impact contact force history and damage area between the analysis results and the experimental data shows the validation of the developed FEM.

Ambient and high temperature in situ damage evolution in nickel based IN 718 super alloy

The mechanical response in compression of several explosives was determined as a function of temperature and strain rate. The compressive strength (maximum stress) and the Young's modulus increase with decreasing temperature and increasing strain rate and are proportional to each other. While the compressive strength and Young's modulus vary by about an order of magnitude, the strain at the maximum stress is approximately constant with variations of strain rate and temperature. This approximately constant strain, which can be used as a criteria for failure, is attributed to damage generation that is a function of strain but not temperature or strain rate.

A recently developed anisotropic model of continuum damage mechanics has been applied successfully to characterize ductile fracture of cracked plates under mode I and mixed mode failures. The damage model is further extended in this investigation to examine its applicability to include notch ductile fracture of thin plates containing a circular hole. Two hole sizes of 16 mm and 24 mm diameters are chosen and the specimen material is aluminum alloy 2024-T3. Fracture loads of the plates are predicted by the damage model and compared satisfactorily with those determined experimentally. This investigation provides an important confirmation that not only the anisotropic model of continuum damage mechanics but also the same failure criterion developed can be effectively employed to characterize both ductile fracture for plates containing an isolated macro-crack or circular hole which would otherwise not be possible using the conventional theory of fracture mechanics. The successful development of the unified approach to characterize ductile failure provides a vital impetus for design engineers in the general application of the theory of continuum damage mechanics to solve practical engineering problems.

A reliable finite element procedure to simulate shear-dominated ductile fractures in large-scale, thin-walled steel structures is still evolving primarily due to the challenges in determining the failure criterion of metal materials under complex stress states. This paper aims to examine the accuracy of the modified Gurson–Tvergaard–Needleman (GTN) model considering the shear failure in simulating the ductile fracture of steel plate structures under quasi-static punch loading. The modified GTN damage models are performed by the ABAQUS user-defined material subroutine (VUMAT). The void-related parameters and shear damage parameters of Xue’s and the N-H modified GTN models are calibrated from test specimens with various geometries corresponding to different stress triaxiality and shearing conditions. The damage evolution associated with shearing of voids in the modified GTN models has strong influences on the stress triaxiality versus plastic strain under complex stress states, especially for the shear-dominated loading conditions. Based on the original GTN model, Xue’s and the N-H modified GTN model with calibrated material parameters, a numerical comparative study examines the ductile fracture of steel non-stiffened plates and stiffened plates under punch loading. Benchmarked against the experimental studies, the numerical simulations demonstrate that the shear-driven void evolution in the modified GTN model imposes significant effects on the load–displacement responses as well as the onset and extension of ductile fractures in steel plates under punch actions. The N-H modified model with calibrated shear damage parameters shows a better correlation with the ductile fractures in steel plates observed in the experiment than the original GTN model and Xue’s modified GTN model. As a result of this study, the modified GTN model considering shear action can be applied for practical applications in the crashworthiness assessment of ship collision and grounding.

Numerical Simulation of the Aluminum 6061-T6 Cutting and the Effect of the Constitutive Material Model and Failure Criteria on Cutting Forces’ Prediction

Incremental forming is an innovative flexible method used for manufacturing of the sheet metal products and brings a great insight for the small-batch-size or customized sheet products. Some experiments show that incremental sheet metal forming can undergo higher deformations than traditional sheet metal forming. The traditional method to evaluate formability like forming limit curve (FLD) etc can’t give the right answer in incremental forming which is subjected to highly non-monotonic serrated strain paths. In this paper, the Lemaitre’ damage model is presented and fully coupled with finite element simulation in commercial software ABAQUS to predict the failure in incremental forming. Results show that the prediction makes a great agreement with the relevant experiments.

This work concerns with two successive modifications of the Lemaitre's damage model tomeet the requirements of formability prediction for today's modern steels. The first one is the quasiunilateraldamage evolution which modifies the damage driving force by scaling the elastic energyrelease rate due to compressive principal stress components. The second one is the shear modificationby which the damage rate is multiplied by a normalized maximum shear stress dependent factor.With the assumption of non-rotating principal axes of deformation, proportional strain paths and rigidplasticity, closed form expressions for the isochronous fracture surfaces are derived for each modelvariant and resulting surface plots at various spaces are compared. The findings show that the formermodification not only remedies the pathological reflective symmetry of the fracture surface acrossthe plane with vanishing stress triaxiality ratio, but also allows hindering fracture under uniaxialcompression. The latter modification by adding a direct Lode parameter dependence to the damageevolution function allows prediction of premature fracture at generalized shear stress states, a conditionobserved for certain advanced high strength metallic sheets. Parameter calibration is realized foreach model variant using the experimental data from the literature. It is shown that the fracture modelwith both the shear modification and the quasi-unilateral enhancement shows the best fitting quality.Finally, the models are implemented as user subroutines for ABAQUS/EXPLICIT and used in predictionof initiation and propagation of cracks for a series of deep-drawing punch tests. A good agreementwith the outputs reported in the literature is observed in terms of the shear damage occurrence zonesas well as corresponding punch force-displacement diagrams.

Coal-based carbon foam (CCF) has broad application prospects in aerospace, composite material tooling and other fields. However, the lack of failure criteria limits its promotion. In previous studies, the failure criteria of similar materials were proposed, but there are some limitations. This paper proposes improved failure criteria based on macro-mechanical tests. Furthermore, uniaxial and multiaxial loading tests were carried out to obtain accurate failure criteria of CCF. Finally, 3-points bending tests of the CCF sandwich structure were conducted and their finite element models (FEMs) were established. The CCF test results show that the mechanical properties of CCF are transversely isotropic. The failure criteria in this paper can accurately predict the stress when the CCF fails. The error band boundary formula caused by the dispersion of the material were also given. The maximum load Pmax calculated by the failure surface (3684 N) was only 4.7% larger than the mean value measured by the test (3518 N), and all of the Pmax measured by the test (3933 N, 3640 N, 3657 N, 3269 N, 3091 N) were between the maximum value (4297 N) and minimum value (3085 N) calculated by the error band boundary formula, which means that the failure criteria have good precision.

This work evaluates the effectiveness of commonly adopted local damage evolution methods and failure criteria in finite element analysis for the simulation of intralaminar damage propagation in composites under static loading conditions. The proposed numerical model is based on a User Defined Material subroutine (USERMAT) implemented in Ansys. This model is used to predict the evolution of damage within each specific lamina of a composite laminate by introducing both sudden and gradual degradation rules. The main purpose of the simulations is to quantitatively assess the influence of the adopted failure criteria in conjunction with degradation laws on the accuracy of the numerical predictions in terms of damage evolution and failure load. The mechanical behavior of an open hole tension specimen and of a notched stiffened composite panel under shear loading conditions have been numerically simulated by Progressive Damage Models (PDM). Different failure criteria have been implemented in the developed Ansys USERMAT, together with sudden and gradual degradation rules based on the Continuum Damage Mechanics (CDM) approach. Numerical results have been validated against experimental data to assess the effects of the different failure criteria and damage evolution law on the global mechanical response and local damage predictions in composite laminates.

This study presents reviews of the failure criteria to capture the resulting response due to the catastrophe of ship collision and grounding using the finite element. Researchers have introduced several failure criteria, for instance, the DNV RP-C204 criterion, Germanischer Lloyd criterion, Peschmann, RiceTracey and Cockcroft-Latham (RTCL), Bressan-Williams-Hill (BWH) instability criterion, and Liu criterion. As in the mathematical formula, each criterion has a difference. The choice of failure criteria will depend on the simulation's specific requirements and the analysis's goals. Liu's criterion can be used to evaluate the failure of materials in ship collision simulations, for example, when large element sizes (i.e., 20 mm) are considered in the simulation.

ABSTRACT: The objective of this paper is to develop a two-dimensional Cohesive Element Model (CZM) coupled with a Continuum Damage Mechanics (CDM) model. The novel cohesive element model allows expressing the separation criterion in terms of the damage tensor used in the CDM model implemented in the neighboring volume elements. Above a critical damage value, debonding triggers. The residual tensile and shearing strength of the CZM follow a linear softening law. The proposed model was calibrated against published triaxial compression tests conducted on shale. Single-cohesive zone tests highlight that the proposed approach allows simulation of hardening during damage propagation followed by softening and failure. The model predicts different strengths in tension and compression and different stiffnesses and strengths for different confinements. A boundary-value problem was solved by using a mesh with embedded cohesive zones at all interfaces. It is shown that the 2D model can predict realistic stress/strain curves, stress and strain fields, and fracture patterns for biaxial compression tests. The advantage of the proposed approach is that it can be used to simulate diffuse damage followed by localized fracture with a smooth transfer of field variables between the finite and cohesive elements. 1 INTRODUCTION Simulating fracture propagation from the inception of microscopic cracks to the localization of macroscopic fractures remains a challenge. To date, finite element modeling approaches based on Continuum Damage Mechanics (CDM) and Cohesive Zone Models (CZM) emerge as the most widely used approaches. The goal of this study is to couple both, in order to take advantage of the benefits that each technique can bring. In CDM, sets micro-cracks are represented by a damage tensor, which is modeled as an internal variable within the framework of thermodynamic irreversible processes. Stiffness and strength decrease as damage accumulates. CDM models can be formulated based on phenomenological principles (Xu and Arson, 2014) or micromechanics principles (Jin and Arson, 2017). Exhaustive reviews of damage rock mechanics are available in (Arson and Gatmiri, 2008; Arson, 2020).

Continuum Damage Mechanics is successfully employed to describe the behaviour of metallic materials up to the onset of fracture. Nevertheless, on its own, it is not able to accurately trace discrete crack paths. In this contribution, Continuous Damage Mechanics is combined with the XFEM and a Cohesive Law to allow the full simulation of a ductile fracture process. In particular, the Cohesive Law assures an energetically consistent transition from damage to crack for critical damage values lower than one. Moreover, a novel interpretation is given to the parameters of the cohesive law. A fitting method derived directly from the damage model is proposed for these parameters, avoiding additional experimental characterization.

Three-dimensional invariant-based failure criteria for fibre-reinforced composites